Suppose you wish to compare the characteristics of tuberculosis meningitis in patients infected with HIV and those who are not infected. In particular, you would like to determine whether the two populations have the same mean age. A sample of 43 infected patients has a mean age of 26.9 years and a standard deviation of 5.3 years; a sample of 23 patients who are not infected has a mean age or 36.1 years and standard deviation of 19.8 years. A. Do you think these two underlying populations have equal variances? Explain in one sentence B. Test the null hypothesis that the two populations of patients have the same mean age at the 0.05 level of significance. Select one With a p-value greater than 0.05, we can reject the null hypothesis at the 5% level. With a p-value less than 0.05, we fail to reject the null hypothesis at the 5% level. With a p-value greater than 0.05, we fail to reject the null hypothesis at the 5% level. With a p-value less than 0.05, we can reject the null hypothesis at the 5% level. C.Would you expect that the 95% confidence interval for the true difference in population means would contain the value 0? Select one Without calculating a confidence interval, we can not answer this. Yes, we reject the value 0 with our hypothesis test. No, we reject the value 0 with our hypothesis test. Confidence intervals never contain 0.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Suppose you wish to compare the characteristics of tuberculosis meningitis in patients infected with HIV and those who are not infected. In particular, you would like to determine whether the two populations have the same mean age. A sample of 43 infected patients has a mean age of 26.9 years and a standard deviation of 5.3 years; a sample of 23 patients who are not infected has a mean age or 36.1 years and standard deviation of 19.8 years.

A. Do you think these two underlying populations have equal variances? Explain in one sentence

B. Test the null hypothesis that the two populations of patients have the same mean age at the 0.05 level of significance. Select one

With a p-value greater than 0.05, we can reject the null hypothesis at the 5% level.

With a p-value less than 0.05, we fail to reject the null hypothesis at the 5% level.

With a p-value greater than 0.05, we fail to reject the null hypothesis at the 5% level.

With a p-value less than 0.05, we can reject the null hypothesis at the 5% level.

C.Would you expect that the 95% confidence interval for the true difference in population means would contain the value 0? Select one

Without calculating a confidence interval, we can not answer this.

Yes, we reject the value 0 with our hypothesis test.

No, we reject the value 0 with our hypothesis test.

Confidence intervals never contain 0.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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